ST. PETERSBURG, Fla. — Even with the trade deadline lurking and his name churning through the rumor mill, Red Sox reliever Andrew Miller isn’t at the point where he’s running his name through search engines to figure out what’s going on.

At the same time, he said, he’s aware that teams around the league have expressed interest in him.

“It’s our job to ignore them and find a way to perform despite them,” Miller said. “Whatever it is with distractions — trade rumors or the guy yelling at you in the bullpen or not getting a call you want or whatever it is — it’s our job as professionals to ignore those and go out and perform.”

His shutdown job in the seventh inning of the Red Sox’s 3-2 win over the Rays on Sunday was part of the 3⅔
clean innings the bullpen weaved together to help the Sox avoid a sweep in their three-game series against their AL East rival.

With Allen Webster filling the hole in the Sox’ rotation left by the Jake Peavy trade, the bullpen was prepared to put in some work. Webster was working on a quick turnaround, getting the call in Pawtucket while he was on his way to breakfast Saturday, then getting to Tropicana Field by the time the Sox were leaving the ballpark Saturday night.

On Sunday, Webster’s pitch count was creeping into the 80s after five innings. He pitched around five walks to hold the Rays to two runs.

But after seeing Evan Longoria tag Webster for a deep fly ball to center field that Jackie Bradley Jr. had to run into the wall to grab with one out in the sixth inning, manager John Farrell figured he’d gotten as much out of Webster as possible.

“Getting to the sixth inning in a two-run game, he set it up for the rest of the ‘pen,” Farrell said.

The bullpen made sure the lead stood up.

After Craig Breslow gave up a one-out single to James Loney in the sixth, Edward Mujica came in and got a pair of fly balls to get out of the inning.

From there, Farrell called on his three most reliable arms to finish the game.

Miller recovered from a leadoff walk to Curt Casali to start the seventh by sitting down the next three hitters he faced, catching Desmond Jennings staring at a fastball down and away to give him 65 strikeouts in 40⅓ innings this season.

“Doesn’t matter how you get there, if there’s a zero on the board at the end of the inning, that’s what matters and I was fortunate to get through it,” Miller said.

Two days after arguably his worst outing since converting to a reliever, Junichi Tazawa bounced back with a 1-2-3 eighth inning.

He needed just 10 pitches to sit the Rays’ 3-4-5 hitters down in order, with pinch hitter Brandon Guyer failing at a bunt attempt and Longoria and Loney both striking out looking.

“Today might’ve been the best stuff [Tazawa’s] had all year and there was conviction to every pitch that he threw,” Farrell said. “I think the other night might’ve been just the result of too many days down, too many days off. But he was outstanding. Good command, power to his stuff, good split, good breaking ball. He was very good.”

After struggling to throw strikes in his last outing, Tazawa started all three hitters he faced with first-pitch strikes Sunday.

“The last couple outings, especially, I was a little bit passive,” Tazawa said. “So I was trying to be aggressive attacking the hitters and I think that was key.”

He built a bridge to Koji Uehara, who struck out the side after giving up a leadoff single. It was his 40th scoreless appearance of the season.

More than a week had passed since his last save, but he earned his 21st of the season, tying the career-high he set in 2013.

One testament to the strength of the bullpen is the Sox’s 37-0 record when leading after eight innings.

“That’s pretty hard to do,” Miller said. “We’ve been pretty good and when you’ve got Koji in the ninth inning, that makes it a lot easier to get out of the eighth inning and finish the ninth.

“We’ve got a lot of weapons, a lot of guys that have thrown well this year. It’s a pretty veteran staff and we seem to find a way.”

Miller intends to do that even with whatever distractions that might come his way this week.

“I’m just trying to go out there and put up a zero and do my job and hand the ball to the next guy,” Miller said.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.